X268

ISOGONAL CONJUGATE OF X196

X268 is the isogonal conjugate of X196.
< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 3, 9 }: Central Line L(3, 9) { 219, 255 }: Central Line L(219, 255) { 21, 280 }: Central Line L(21, 280) { 220, 577 }: Central Line L(220, 577) { 281, 1012 }: Central Line L(281, 1012) { 222, 1073 }: Central Line L(222, 1073) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_196 = -CEVA CONJUGATE OF X(4) (0.5649, -0.1989) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_9 = MITTENPUNKT (0.5110, 0.1615) X_219 = -CEVA CONJUGATE OF X(55) (0.4277, 0.0625) X_255 = ISOGONAL CONJUGATE OF X(158) (0.4217, 0.0365) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_280 = -CROSS CONJUGATE OF X(8) (0.6379, 0.8041) X_220 = -CEVA CONJUGATE OF X(55) (0.4826, 0.1278) X_577 = HARMONIC OF X(216) (0.4663, 0.0464) X_281 = -CROSS CONJUGATE OF X(9) (0.5796, 0.3202) X_1012 = INTERCEPT OF EULER LINE AND LINE X(1)X(84) (0.5770, 0.3036) X_222 = -CEVA CONJUGATE OF X(56) (0.5653, 0.1568) X_1073 = -CROSS CONJUGATE OF X(3) (0.4792, -0.4343) X_268 = ISOGONAL CONJUGATE OF X(196) (0.7710, 1.5678) A B C X196 X3 X9 X219 X255 X21 X280 X220 X577 X281 X1012 X222 X1073 X268 (a, b, c) = (5, 6, 7) | AB = 1

X268 (ISOGONAL CONJUGATE OF X196) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(A,B,C) : f(B,C,A) : f(C,A,B)\), where \(f(A,B,C) = (\cos A \cot A/2)/(-1 - \cos A + \cos B + \cos C)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(3.669332046882\)
▸ Incident Central Lines6 lines

{3, 9}, {21, 280}, {219, 255}, {220, 577}, {222, 1073}, {281, 1012}

▸ Functional Relations4 relations